
theorem Th6:
  for x being Real st x in DYADIC holds for n being Nat
  st inf_number_dyadic(x) <= n holds x in dyadic(n)
proof
  let x be Real;
  assume x in DYADIC;
  then
A1: x in dyadic(inf_number_dyadic(x)) by Th5;
  let n be Nat;
  assume inf_number_dyadic(x) <= n;
  then dyadic(inf_number_dyadic(x)) c= dyadic(n) by URYSOHN2:29;
  hence thesis by A1;
end;
